Name
Abstract | ||
|---|---|---|
Continuing previous work, we discuss applications of our summation/integration procedure to some classes of complex slowly convergent series. Especially, we consider the series of the form
<img src="/fulltext-image.asp?format=htmlnonpaginated&src=385136G2941Q0252_html\11075_2005_Article_BF02198299_TeX2GIFIE1.gif" border="0" alt="
$$\sum\nolimits_{k = 1}^{ + \infty } {( \pm 1)^k k^{v - 1} } R(k)$$
" />, where 0v≦1 andR(s) is a rational function. Such cases were recently studied by Gautschi, using the Laplace transform method. Also, we give an appropriate method for calculating values of the Riemann zeta function
<img src="/fulltext-image.asp?format=htmlnonpaginated&src=385136G2941Q0252_html\11075_2005_Article_BF02198299_TeX2GIFIE2.gif" border="0" alt="
$$\zeta (z) = \sum\nolimits_{k = 1}^{ + \infty } {k^{ - z} } $$
" />, which can be transformed to a weighted integral on (0,+∞)of the functiont → exp (−z/2)log(1-β |
Year | DOI | Venue |
|---|---|---|
1995 | 10.1007/BF02198299 | Numerical Algorithms |
Keywords | DocType | Volume |
Primary 40A25,Secondary 30E20,65D32,33C45 | Journal | 10 |
Issue | Citations | PageRank |
1 | 0 | 0.34 |
References | Authors | |
0 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gradimir V. Milovanović | 1 | 45 | 11.62 |